Structural Engineering & Statics
where the load goes
Concept

Directional method — where it appears

The exact check on a fillet weld, made on the stresses resolved onto its throat. The normal and two shear components are combined by von Mises and compared with the weld metal's strength, which gives a capacity depending on the direction of the force — from the along-the-weld value to √1.5 times it across.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

A fillet weld is stronger across than along. Capacity of a 4 mm throat over 100 mm, against the angle between the weld's axis and the load. Loaded along its length it carries 116.83 kN; loaded across it, 143.09 kN. The ratio is 1.22, which is √3/√2 exactly, and it comes out of the failure criterion rather than out of a test.

The weld that is stronger across than along

The same fillet weld, the same size, the same steel, carries twenty-two per cent more when the load runs across it than along it. The factor is exactly the square root of three over the square root of two, and it comes out of the yield criterion rather than out of a test.

connections · Weld strength Force and capacity round a weld group, which do not vary together. Utilisation round the c shape group under 100 kN at 150 mm, walked from one end of the weld to the other, with the force scaled onto the same axis for comparison. The capacity is 1460 N/mm where the force runs along the weld and 1789 where it runs across it — √1.5 more — so the utilisation is not simply the force in different units. The worst point is at 47 degrees to the weld, where the capacity is 1612 N/mm, and the group carries 182 kN against the 165 the along-the-weld value would allow.

The weld that is stronger where it is pulled

A fillet weld pulled across its axis is √1.5 stronger than the same weld pulled along it. On a group under an eccentric load the direction of the pull varies from point to point, so the capacity does too — and the gain that follows is worth twenty per cent at one eccentricity and nothing at all at another.

connections · Weld strength Made from one side, the throat misses the load and its root takes the difference. Two plates 20 mm thick joined by a partial-penetration butt weld with 10 mm of throat, pulled apart by a force on their mid-thickness, with the stress across the throat drawn beside each joint as a multiple of the mean. Above, welded from one side: the throat runs from the top face down to 10 mm, so the force passes 5.0 mm below its centroid. The moment adds tension at the root and removes it at the face: the root carries 4.00 times the mean stress and the face −2.00, which is compression. The unfused 10 mm below the root is a notch, and it is on the tension side. Below, the same 10 mm of throat split between the two faces: the force passes through its centroid and every part of it carries the mean stress.

The throat that misses the load

A partial-penetration butt weld's throat faces the load squarely, so a millimetre of it carries more than a fillet's, and in every grade what limits it is a cap on normal stress rather than the directional criterion. Made from one side, the throat sits off the plates' line of action. At half penetration it keeps a quarter of that capacity, and the stress the eccentricity adds lands on the root, which is a crack.

connections · Weld strength A butt throat is strongest a little off square. The resultant a millimetre of throat can carry in S355 against the direction of the load, from straight across the weld (0°) to straight along it (90°). The fillet's falls throughout, from 385 to 314 N/mm². The butt's rises from 441 to 478 at 22.7°, because its cap limits only the normal stress and a little shear costs it nothing, and then falls to 314. So the butt's advantage over the fillet is 1.15 straight across, 1.29 at 22.7°, and none straight along.

The shear that helps a butt weld

A partial-penetration butt throat pulled straight across its weld is capped at 0.9fu, which in S355 makes it 15 per cent stronger than a fillet throat. Add a little shear along the weld and the butt throat gets stronger, not weaker, because the cap limits only the normal stress — until the shear is 42 per cent of the pull, where it is 29 per cent stronger than the fillet and carries its largest resultant, 478 N/mm² against 441 straight across. Along a moment connection's web weld the mix of pull and shear sweeps through that peak, and in the direction that is all shear a single-sided throat is as good as two.

connections · Weld strength The single side's strongest direction is not the double side's. The resultant a millimetre of throat can carry in S355 against the direction of the load: a double-sided butt throat, a fillet throat, and a 20 mm plate's single-sided throat at penetrations of 0.5 and 0.7, counted plastically. The double-sided butt is strongest at 22.7°, 478 N/mm². The single side at 0.5 rises from 183 straight across to 314 straight along and is strongest along the weld; at 0.7 it rises from 291 to 357 at 40° and falls to 314, and from 38° to 88° it carries more than the fillet.

The root that has to stretch for it

A partial-penetration weld made from one side carries its pull off the plates' line, and counted elastically it keeps a quarter of a double-sided weld at half penetration. Let the throat yield and it keeps 0.41 — but the same 0.41 at every direction up to the one where the double-sided weld is strongest, so that weld's peak advantage is never won back. What the yielding does instead is move the single side's own strongest direction out to 40° or beyond, where a deep single-sided throat outcarries a fillet. Every per cent of it is paid for with strain at the root, which is the tip of an unfused land.

connections · Weld strength

Named alongside it

The objects these essays reach for when they reach for this one.

EccentricityWeld strengthWeld throatConnection designDuctilityStress combinationVon misesDetailingFillet weldShear stressYield criterionConnection

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